A337798 - OEIS

%I #16 Dec 25 2021 02:41:01

%S 1,1,1,1,1,1,1,1,1,2,1,1,3,1,1,2,4,5,4,5,7,11,9,4,12,12,24,23,42,59,

%T 64,58,124,206,212,168,377,539,703,873,1122,1505,1943,2724,4100,4513,

%U 6090,7138,12079,16584,20240,27162,35874,52622,69817,88059,115628,152756,219538,240200,358733,480674

%N Number of partitions of the n-th n-gonal pyramidal number into distinct n-gonal pyramidal numbers.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>

%F a(n) = [x^p(n,n)] Product_{k=1..n} (1 + x^p(n,k)), where p(n,k) = k * (k + 1) * (k * (n - 2) - n + 5) / 6 is the k-th n-gonal pyramidal number.

%e a(9) = 2 because the ninth 9-gonal pyramidal number is 885 and we have [885] and [420, 266, 155, 34, 10].

%p p:= (n,k) ->  k * (k + 1) * (k * (n - 2) - n + 5) / 6:

%p f:= proc(n) local k, P;

%p   P:= mul(1+x^p(n,k),k=1..n);

%p   coeff(P,x,p(n,n));

%p end proc:

%p map(f, [$0..80]); # _Robert Israel_, Sep 23 2020

%o (PARI) default(parisizemax, 2^31);

%o p(n,k) = k*(k + 1)*(k*(n-2) - n + 5)/6;

%o a(n) = my(f=1+x*O(x^p(n,n))); for(k=1, n, f*=1+x^p(n,k)); polcoeff(f, p(n,n)); \\ _Jinyuan Wang_, Dec 21 2021

%Y Cf. A006484, A288126, A298857, A337763, A337797, A337799.

%K nonn

%O 0,10

%A _Ilya Gutkovskiy_, Sep 22 2020

%E More terms from _Robert Israel_, Sep 23 2020